Problems with the baggage system at Terminal 5 between Thursday and Sunday meant that thousands of British Airways passengers’ bags were not loaded onto their flights.

A Heathrow spokeswoman said the computer glitch meant some bags had to be processed manually, which “led to some bags not making flights in time”.

BA – the only airline to operate from the terminal –said it has been working “around the clock” to reunite customers with their bags, and that all bags had been dispatched by the end of Tuesday.

However, it added that the nature of international travel, complex security issues and customs regulations meant that it may still take several days for passengers to receive their belongings.

Travellers have been expressing frustration and anger at the way BA has handled the situation.

Alison Gayer and Phil Jackson travelled to Colombia with three other friends on Thursday for a two-week multi-stop holiday, flying to Miami with BA and then taking a connecting flight to Bogota with Avianca. Upon arrival, they discovered that none of their bags had arrived, and it was only on Saturday that they realised the problem was not due to Avianca but because of the IT problems at Heathrow, but said this had not been communicated to them by BA or the airport.

Mr Jackson said BA customer service representatives had been "devoid of any initiative" and at times rude.

As of Wednesday evening, the group has been reunited with four of their five bags, but because the luggage problems meant they missed connecting flights during their two-week holiday in Colombia, they said they had been "denied experiences that we will probably never get back."

"We all work extremely hard and have spent the first six days, and potentially countless more, of our holiday stressed and feeling like we are doing the jobs of the people that should be resolving this for us," said Mr Jackson.

British Airways has said that all the remaining bags are en route to customers. The member of the group without his luggage had been attempting to continue his holiday without his main bag.

A British Airways spokesperson told Telegraph Travel that they have drafted in extra staff to try to reunite customers with their baggage as soon as possible, including in contact centres, which had extended opening hours. Because of the need to process the bags manually, British Airways explained that it did not have the normal level of information about luggage whereabouts to pass on to customers.

“We understand this has been very frustrating for customers, and we are sorry for the difficulties this has caused,” the spokesperson added.

One Twitter user complained to British Airways about the inefficiency of the online claims system, saying that the claims site showed a “system error”. British Airways responded with a link to the claims form.

As Telegraph Travel’s consumer expert Sophie Butler has written, airlines are obliged to cover costs of “essential items” such as underwear and toiletries, for which compensation should come in the form of an upfront cash payment, a fixed daily budget or remittance once your claim and receipts have been submitted, normally to a value of £100-£200. She cautioned against immediately taking up the issue with travel insurance providers, something that airlines may encourage.

In general terms, passengers whose bags never turn up may claim up to £1,100 under the terms of the Montreal Convention, a treaty setting out rights for victims of air travel issues. It is widely recommended that air travellers always carry some essentials in their hand luggage, in the event that their baggage does go missing.

Heathrow said: "We are very sorry for the disruption passengers have experienced and we are working round the clock with airlines to reunite passengers with their bags as quickly as possible."

A Heathrow statement added that passengers are still able to check in bags, and flights are operating normally, without delays.